1. Field of the Invention
The present invention generally relates the field of signal-dependent noise estimation. More particularly, the present invention relates to an apparatus and method for estimating signal-dependent noise using wavelet coefficients of a low frequency band.
2. Description of the Related Art
Typically, noise is created in the process of image acquisition to image delivery to a final user due to many factors. The factors include the sensor features of a Charge Coupled Device (CCD), hardware features of a camera, and the characteristics of a transmission line. A noise-added image, which is a distortion of an original image, degrades image quality and decreases the performance of secondary image processing operations such as image improvement, information extraction, and object recognition. Noise cancellation from an image is essential to the field of image processing applications. Therefore, noise cancellation is one image processing field that has been studied for a long time and it is viewed as a necessary preliminary process for processing various images.
The most general model of image noise takes the form of a conventional image signal and independent noise added to it.Y(i,j)=X(i,j)+σδ(i,j)  (1)                where (i,j) denotes coordinates in an image,                    Y denotes a measured pixel value,            X denotes an original pixel value free of noise,            δ denotes a standard Gaussian random variable, and            σ denotes the standard deviation of the standard Gaussian random variable.                        
Thus, the second term on the right side in equation (1) represents a noise component.
To cancel the independent noise from a conventional image signal as represented in equation (1), wavelet transform is usually adopted. The wavelet transform verified its usefulness in X-ray and magnetic resonance image processing in the medical field. A clear image without blurs in details can be obtained by the wavelet transform. A weak signal can be recovered from noise by use of the wavelet transform. The wavelet transform scheme is characterized in that it decreases wavelet coefficients including noise components sufficiently, while it decreases wavelet coefficients including signal components as little as possible or keeps them unchanged.
That is, noise cancellation in a wavelet area amounts to reduction of the magnitudes of wavelet coefficients contaminated with noise. A noise-added image is wavelet-transformed and the magnitudes of wavelet coefficients are adjusted or small wavelet coefficients are eliminated. Then inverse wavelet transform is performed, resulting in a cancellation of the noise component.
The standard deviation or variance of noise is the most significant part of wavelet transform-based noise cancellation. Since the variance of noise is not known beforehand in most cases, it should be estimated from an image having a noise component. To do so, a median noise estimator is used. The median noise estimator wavelet-transforms the image and then estimates the noise variance from the coefficients of the diagonal components in the highest frequency band.
Although the median noise estimator brings very accurate results for the signal and the independent noise expressed as equation (1), it has limitations in its effectiveness in estimating signal-dependent noise as observed in a camera module.
A more accurate noise model for an image obtained from Complementary Metal Oxide Semiconductor (CMOS) and CCD sensors in a camera module can be expressed asY(i,j)=X(i,j)+(k0+k1X(i,j))δ(i,j)  (2)                where k0 and k1 are positive constants representing characteristics of a camera.        
According to this model, the standard deviation of noise is larger in pixels with higher brightness values.
Equation (2) is referred to as a signal-dependent noise model in which the variance of noise is not independent of the signal X. In general, the CCD and CMOS sensors create noise due to light intensity or heat in view of their natures. This noise does not take Gaussian (or Laplacian) statistical characteristics and is dependent on the signal, compared to the general noise model. Hence, the noise of the sensors is not white and thus it is not easily eliminated by a general noise cancellation algorithm. Even though eliminated, the noise severely damages high frequency components of the signal.
As described above, the variance of the noise expressed as equation (2) is dependent on the original signal X. Even when the observed image is subject to wavelet transform, a part corresponding to the noise still has information about the original signal X. Thus, the value of the original signal X is required for estimating the noise variance and the noise cannot be estimated reliably with the median noise estimator.